This phase I/II trial studies the side effects and best dose of bortezomib when given together with melphalan, and total-body irradiation before stem cell transplant and to see how well it works in treating patients with multiple myeloma. Giving chemotherapy and total-body irradiation before a stem cell transplant stops the growth of cancer cells by stopping them from dividing or killing them. The stem cells that were collected from the patient's blood or bone marrow are returned to the patient to replace the blood-forming cells that were destroyed by the chemotherapy and total-body irradiation.